How do I adjust bone rotation_mode when freshly created armature has pose = None (python)
LucaRood in IRC was the first one to suggest using scn.update() after the link().  batFINGER and my testing agree with that solution.  So the proper code would be

import bpy

scn = bpy.context.scene
obj = bpy.data.objects.new('garbage', bpy.data.armatures['lids_armature.007'])
scn.objects.link(obj)

scn.update()
obj.pose.bones[0].rotation_mode = 'XYZ'